Yesterday, Google announced that it would be tweak its search results to downrank sites that had high numbers of takedown requests, a sign that they could be hosting pirated files. But as Search Engine Land explains, this change isn't likely to hurt its own YouTube service, which also has a high takedown volume. That's because YouTube has a different content removal system than the standard content removal form used for Search. So when a video is flagged for removal, it appears to be counted as a takedown in YouTube, but not Seach, and other YouTube results aren't in danger of getting downranked as a result.
Google has responded, saying that it isn't giving its own sites special dispensation. "We’re treating YouTube like any other site in search rankings. That said, we don’t expect this change to demote results for popular user-generated content sites." It's possible Google will take YouTube removal requests into account when calculating its downranks, but for now, requests for YouTube or Blogger don't even show up on the public copyright notices report.
Update: Google has clarified that takedown requests submitted through YouTube and Google search are counted together in the new rankings, and that the site is indeed not receiving preferential treatment.